Empirical insights into the distress risk anomaly: evidence from India

Abstract

Purpose

This paper aims to examine the relationship between financial distress risk and stock returns in the Indian context.

Design/methodology/approach

This is an empirical study wherein the Altman-Z score is used to identify the distressed and the non-distressed firms listed on Nifty 500. The author uses the Fama–French five-factor model to study the relationship between stock returns and distress risk. The study analyses the differences in the factor loadings among the portfolios sorted by distress. It evaluates if incorporating distress risk factors in conventional pricing models enhances the goodness of fit.

Findings

The study reported a positive relationship between the distress risk factor and stock returns in the distressed portfolios, signifying that distress risk is a systematic risk only for distressed portfolios. Furthermore, after including the financial distress risk premium, the observed fluctuations in the small-minus-big (SMB), high-minus-low (HML), RMW and CMA coefficients indicate a common association with distress risk-related information.

Originality/value

This study tests the Fama–French five factors for distress risk and examines its nature in asset pricing for emerging markets like India. The study examined the performance of the augmented Fama–French five-factor model across different sets of portfolios sorted based on distress.

Citation

Singh, P. and Chakraborty, A. (2024), "Empirical insights into the distress risk anomaly: evidence from India", Vilakshan - XIMB Journal of Management, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/XJM-04-2024-0067

1. Introduction

Asset pricing research seeks to explain why and how asset prices are established, with the efficient market hypothesis (EMH) theory at its core. A market is efficient when asset prices account for all available information (Fama, 1970). The EMH offers a widely accepted framework for evaluating asset prices and elucidates the rationale behind the unpredictability of asset returns. However, empirical research has called into question the market’s efficiency, the core of asset pricing models, arguing that asset values are predictable with diverse fundamental business features that allow investors to generate excess returns (Novy-Marx and Velikov, 2016; Basu, 1977; Banz, 1981). The recent period has witnessed a mounting focus and discussion among scholars, investors and financial authorities concerning the importance of financial distress risk within the stock market. Understanding the various factors that influence stock returns is critical, particularly in the context of developing economies (Quy Duong and Bertrand, 2022; ElBannan, 2021) like India, which are known for their complexity and volatility. Compared to more traditional criteria, such as market volatility and trading volumes, the risk associated with financial distress is often neglected (Novy-Marx and Velikov, 2016; Basu, 1977; Banz, 1981).

1.1 Conceptual underpinnings

The concept of distress risk implies that firms are more likely to be incapable of meeting their existing financial obligations. If this risk is mainly non-diversifiable, investors will expect higher returns as a reward for holding these companies’ stocks. Cochrane (2005) contended that idiosyncratic distress cannot provide a risk price. Hence, it must be considered an aggregate macroeconomic issue in rational asset pricing that remains inexplicable by the capital asset pricing model (hereafter CAPM).

1.1.1 Nature of the relationship between distress risk and stock returns.

In the empirical literature, two primary strands present conflicting results concerning the direction and importance of this distress risk and return relationship. Vassalou and Xing (2004), Chava and Purnanandam (2010), Ferreira Filipe et al. (2016), Anginer and Yildizhan (2018) and Asis et al. (2021) have observed a positive correlation between distress risk and stock returns. Conversely, multiple studies have identified a negative relationship between distress risk and returns, sometimes referred to as the distress anomaly (Liu et al., 2023; Dichev, 1998; Griffin and Lemmon, 2002; Agarwal and Bauer, 2014; Gao et al., 2019).

1.1.2 Distress risk and other anomaly relationship.

Chan and Chen (1991) and Fama and French (1992) contended that the size and value premium arise as compensation for distress risk. They maintained that weak companies with consistently low earnings have high book-to-market values and positive slopes on high-minus-low (HML), and that small companies typically have limited access to external financing and unstable cash flows, which implies the importance of the small-minus-big (SMB) factor in proxies for distress risk. The distress risk and returns relationship was first studied by Dichev (1998). After accounting for size and book-to-market, the study discovered a negative link between default risk and returns within the cross-sectional Fama–MacBeth (1973) regression framework. The study concluded that bankruptcy risk is not rewarded by higher return; hence, it is an unsystematic risk, and the size and book-to-market effects are unlikely to be due to a distress factor related to bankruptcy risk. Zaretzky and Kenton Zumwalt (2007) also found the relation between distress risk, book to market and return inconsistent. Campbell et al. (2008) used a wide range of accounting and equity market characteristics to evaluate distress risk and discover that returns on growth and value companies are negatively associated with default risk.

Similarly, Gao et al. (2018) explored the distress risk anomaly. They found a robust negative relationship between default probabilities and equity returns concentrated among low-capitalisation stocks in developed North American and European countries. Avramov et al. (2022) also confirmed that high credit-risk companies’ bonds and stocks have abysmal returns.

Denis and Denis (1995) partially supported the role of HML and SMB as pricing factors for default risk because their pertinence depends on macroeconomic circumstances and the business cycle. Zhang (2005) also considered the SMB and HML factors of Fama and French (1992) to be priced risk factors. Unlike non-distressed firms, distressed firms earn higher returns because of the high loadings on the size and value factors (Bauer, 2012). Besides, studies such as de Groot and Huij (2018) and Gharghori et al. (2007) asserted that while size and value risk factors contain some information about distress, they claim that these factors earn a premium primarily due to distress risk being inconsistent. Although several studies show that value and small-cap stocks provide abnormal returns, Anginer and Yıldızhan (2018) inferred that stocks with higher credit risk premia have higher expected equity returns. The market, size and value factors largely explain the premium to an HML systematic default risk hedge portfolio. Avramov et al. (2022) state that the anomaly is an unresolved puzzle, and it remains unclear from empirical evidence whether the small-cap and value anomalies are linked to financial distress.

Furthermore, based on the findings of Novy-Marx (2013) and Aharoni et al. (2013) Fama and French (2015) documented that stock returns are determined not just by the market, market capitalisation and valuation but also by profitability and investment patterns. They used the dividend discount model to explain how profitability and investment contribute to the understanding of average return. The concept posits that the market value of a stock share is the present value of expected dividends per share. According to Hou et al. (2015), “many seemingly unrelated anomalies turn out to be different manifestations of the investment and profitability effects”. De Groot and Huij (2018) investigated if these factors are related to distress risk in some ways and contradicted the notion that the profitability premium is due to distress risk. They reported similar findings for investment premiums, too. However, Khan and Iqbal (2021) stated that the investment factor (i.e. CMA) comprises some default-related information.

Despite the extensive study of the distress risk anomaly, there still needs to be more consensus on its underlying causes and implications. Besides, most empirical research concentrates on developed economies having more developed financial markets than developing economies. The latter markets have high transaction costs, low asset marketability, instability and low informational efficiency (Mosoeu and Kodongo, 2022), providing an alternative ground to test the distress risk puzzle. India was selected for the study as it is a fast-growing emerging economy with strong global connections. A number of studies have been conducted within the Indian context to analyse distress risk, like Saji (2018) and Sareen and Sharma (2022), but these studies are confined to specific sectors like real estate or automobile, while Nedumparambil and Bhandari (2020) studied the credit risk puzzle in India using the Fama–French three-factor model and the Carhart four-factor model. This study extends the existing literature by examining the Fama–French five factors as a proxy for distress risk and the nature of the distress risk factor in the context of the asset pricing framework. The study also examined the performance of the augmented Fama–French five-factor model across different sets of portfolios.

1.1.3 Objectives of the study.

• to examine the relationship between distress risk and stock returns for firms listed on Nifty 500;

• to examine the relationship of distress risk with the Fama–French risk factor; and

• to examine whether including an additional distress risk factor enhances the performance of the Fama–French five-factor model.

The paper is structured as follows: Section 2 summarises the research methodology, Section 3 presents results and discussion and the final section covers the conclusion and implication, the study’s limitations and the scope for future research.

2. Data and methodology

The research has been conducted on the non-financial companies in the Nifty 500 index, which comprises 95% of the market capitalisation of firms listed on India’s National Stock Exchange (NSE) and is considered the most representative of the whole market. The study encompasses ten years, specifically 120 months, from 2011 to 2012 to 2020–2021. Financial institutions are excluded due to their unique financial characteristics. Further, the firms for which accounting data are missing are also eliminated from the study. The final sample consisted of a total of 221 companies. The study sourced financial data from the CMIE PROWESS database, while Nifty 500 index closing price data was retrieved from the NSE website. Additionally, the Reserve Bank of India’s database was used to obtain a 91-day treasury bill rate, serving as a risk-free rate indicator.

2.1 Methodology

2.1.1 Measure of financial distress.

Following Zhang (2022) in this study, Altman’s (1968) Z-score has been used to predict financial distress. The Z-score took into account five ratios to predict a firm’s financial distress:

Z=1.2X1+1.4X2+3.3X3+0.6X4+1.0X5

Kindly refer to Table 1 for each variable description.

2.1.2 Model specification.

The following models are taken into consideration for unravelling distress risk premium:

Here, Ri, Rf and Rm are the return of portfolio (i), risk-free and market portfolio returns, respectively. α is the regression intercept of the portfolio; b₁, b₂, b₃, b₄, b₅ and b₆ are regression coefficients of the different risk factors (rm-rf); SMB, HML, CMA, RMW and RD that represent the market, size factor, value factor, investment factor, profitability factor and relative distress risk premiums, respectively; for further description, refer to Table 2 and Table 3.

2.1.3 Portfolio construction.

This study examined four portfolios formed on the basis of distress measures for which quartile breakpoints are calculated yearly, as also used in Mosoeu and Kodongo's (2022) study. Using Altman’s Z score, the firms were ranked from lowest (P1) to highest distress risk (P4). Following Sharma et al. (2021) monthly equally weighted returns are calculated for all portfolios from October of the year “T” to September of the year “T + 1”, and portfolios are rebalanced annually. In alignment with Fama and French (1993, 2015) and Singh et al. (2023), portfolios are constructed in September of each year, incorporating a lag of six months to ensure data availability and avoid look-ahead bias.

3. Result and discussion

3.1 Descriptive statistics

Table 4 represents independent variables and shows the monthly per cent excess returns for the chosen risk factors. The risk premiums associated with the distressed portfolio RD are (2.10%), 0.41% for excess market return, 1.72% for SMB, 0.22% for HML and 0.44% for RMW portfolios are positive. By contrast, it is negative for CMA (–0.0036%), implying that CMA’s investment strategy seems to underperform.

3.2 Correlation matrix

Table 5 presents multicollinearity diagnostic statistics for the six risk factors. All explanatory risk factors have VIFs that are less than 10, which confirms that multicollinearity is not a problem in this study (Mselmi et al., 2019).

3.3 Factor spanning test

A factor-spanning test determines whether a factor is redundant in explaining stock returns. The significant intercept value in the factor-spanning result in Table 6 exhibits that the distress factor is not redundant. The distress factor relates negatively but insignificantly to RMW as the distressed strategy is focused on buying stocks of struggling companies with a chance of recovery (Racicot and Théoret, 2016).

3.4 Model performance summary

The GRS test is widely recognised as the predominant statistical method for evaluating the empirical soundness of asset-pricing models. Its null hypothesis is that the intercept terms of empirical asset-pricing equations are jointly equal to zero. Table 7 shows that the augmented five-factor model (MKT SMB HML RMW CMA RD) produced the lowest GRS test value. The Fama and French five-factor and augmented five-factor models leave the unexplained 27% and 32% of the cross-section variance of expected returns. The average absolute pricing error test and other pricing error statistics indicate that the Fama–French five-factor model better describes the average excess return of distress-sorted portfolios. The augmented model has the lowest mean alpha (0.02) across four sets of portfolios. In terms of goodness of fit, the augmented five-factor model (adjusted R² = 0.92) provides a better description of distress measure sorted portfolio than the other models.

3.5 Distress risk and portfolio returns

3.5.1 Single sorting result.

Every month, from October 2012 to September 2022, the securities are sorted into quartiles based on the Altman Z score; Portfolio 1 has the highest Z score, while Portfolio 4 has the lowest Z Score. Table 8 exhibits that the difference between the mean equally weighted return of the high-distress-risk (P4) portfolio and the low-distress-risk portfolio (P1) is 2.2% per month. This study shows a statistically significant difference in returns at a 5% significance level, with a t-value of 2.50. This may indicate that distress risk is priced into stock returns.

3.5.2 Regression result.

One of the primary purposes of this part of the empirical analysis is to test for a systematic relationship between distress risk and equity returns. It is evident from Table 9 that the coefficient of market beta is significant for all portfolios in all models. The insignificant intercept of portfolios P3 and P4 is observed in the augmented Fama–French five-factor model (Aff5), which states that the augmented model captures the expected returns. However, the significant intercept for P1 and P2 portfolios evidences the weaknesses of models in capturing the expected returns. The significant coefficient of SMB explains the presence of the size effect. However, the size premium becomes insignificant in the augmented Fama–French model. The value and CMA coefficient are indistinguishable from zero for a portfolio of the sound firm (P1) in all four models. The profitability premium is found to be significant in both the Fama–French five-factor (FF-5) model and the augmented FF-5 model. The relative distress premium is found to be insignificant in all the models for P1. A similar result is also found for P2. In the case of P3, the size premium is present in all models. The HML becomes insignificant for all models. The relative distress premium is found to be significant in all the models for P4. For the distressed portfolio (P4), all the variables are positive and significant except for RMW. The CMA becomes insignificant in the all augmented Fama–French five-factor model except for P2. From the above result, it can be inferred that all portfolios’ returns are positive and significant, except for P1, where the distress premium slope is positive but insignificant, as explained by the relative distress factor (RD). This means that investors tend to command a higher risk premium to compensate for the distress risk. The distress risk may not be a systematic risk as it only explains the return of three portfolios, i.e. P2, P3 and P4; this result is consistent with Boubaker et al. (2018) and Nedumparambil and Bhandari (2020).

4. Findings and discussion

In congruence with Boubaker et al. (2018), Asis et al. (2021) and Duong et al. (2022) study, we found a positive relationship between financial distress risk factors and stock return. However, the result contradicts the study of Nedumparambil and Bhandari (2020) and Singh and Singla (2023), where a negative relationship between the two was found in the Indian stock market. The reason behind this incongruence could be the difference in the sample period. Further, the study found that the distress premium factor is significant only for the distressed portfolio in the univariate sort based on distress. In other words, the distress risk premium is significant only for distressed portfolios; the result is in line with Boubaker et al. (2018) and Mselmi et al. (2019).

Moreover, the augmented Fama–French five-factor model better captured the expected returns for the portfolio distressed portfolios P3 and P4. The observed fluctuations in the coefficients of SMB and HML, after the inclusion of the financial distress risk premium, indicate a common association with distress risk-related information (de Groot and Huij, 2018; Mselmi et al., 2019; Vassalou and Xing, 2004). A similar result is also found for RMW and CMA factors in the presence of distress risk factors.

Besides, the findings support the proposition that the Fama–French five criteria partially capture the distress risk, albeit not comprehensively, which aligns with the study of Jiang et al. (2017) and de Groot and Huij (2018). The presence of a negative Jensen alpha in some portfolios signifies underperformance of the portfolio concerning the expected risk–return relationship (Fama and French, 2007).

5. Conclusion

The fundamental assumption of asset pricing theory is that risk and return always correlate positively. Several initial empirical studies have found a negative relationship between distress risk and returns, frequently referred to as the distress risk anomaly in academic literature (Avramov et al., 2022; Liu et al., 2023). This study examined the intricate matter in the Indian stock market using the augmented Fama–French five-factor model. It determined that the distress risk is systematic exclusively for the distressed portfolio and inconsequential for the non-distressed portfolio. This is because the distressed portfolio comprises of distressed enterprises, and the risk cannot be further diversified. This finding indicates that, on average, the market expects and implicitly requires more significant returns as compensation for individuals who decide to invest in stocks with a higher level of financial distress risk. The superior returns observed in distressed companies in emerging countries like India could be due to a lack of information transparency or less takeover-friendly legislation (Eisdorfer et al., 2018).

5.1 Implications, limitations and future scope

This study highlights the significance of distress risk in investing, emphasising financial advisers and managers need to understand its impact on returns and develop strategies for distressed portfolios, particularly in emerging economies like India. This knowledge can enhance investors’ decision-making and provide unique insights for Indian and global investors. Since the study period was only ten years, the research outcomes may be influenced by one significant economic event that exhibits prominent characteristics. Therefore, the findings of this study may only apply to the specific timeframe used. Furthermore, the study only augmented the Fama–French five-factor model with the distress factor and did not consider the alternative factor model. Future research should consider alternative factor models like the six-factor model and examine the empirical explanatory power of SMB, HML, RMW and CMA factors while imposing distress-risk neutrality. Testing a distress premium in other emerging markets will also strengthen the study’s validity.

Table 1.

Altman’s Z score variables description

Variables	Description
X1 = Working Capital/Total Assets (WCTA)	It assesses the liquidity status of a company
X2 = Retained Earnings/Total Assets (RETA)	It evaluates the overall profitability and leverage of a company over a period of time
X3 = Earnings before Interest and Taxes/Total Assets (EBITTA)	It measures the firm’s asset productivity
X4 = Market Value of Equity/Book Value of Total Liabilities (MVBTL)	It measures a company’s assets’ relative worth and overall liabilities
X5 = Sales/Total Assets (SalesTA)	It measures the earning capacity of a firm to total assets
Z = overall index	The lower the Z score, the higher the risk of financial distress

Source: Researchers’ compilation

Table 2.

Description and computation of variables

Variables	Proxy	Description
SIZE	Market capitalisation	It is computed by multiplying the stock price by the number of shares outstanding as of the end of September of the year
Value	Book-to-market equity	It is the inverse price-to-book ratio as of March’s end-of-year t
Profit	Operating profit	It is the ratio of operating profit to book equity as of March end of each year t
Investment	Total asset growth	It is the increase or decrease in total assets from March end of year t to March end of year t + 1, divided by the total assets at the end of year t
Relative distress premium (RD)	Altman Z score	It is the difference between the distressed firms portfolio and safe (non-distressed) firms portfolio on the basis of the Altman Z score at the March end of year t

Source: Researchers’ compilation

Table 3.

Formula for factor calculation

Factors	Method
SMB	[(SH+SL) - (BH+BL)]/2
HML	[(SH+BH) - (SL+BL)]/2
RMW	[(SR+BR) - (SW+BW)]/2
CMA	[(SC+BC) - (SA+BA)]/2

Source: Researchers’ compilation

Table 4.

Descriptive statistics

Variable	Mean	SD	Min	Max	Sharpe ratio
rm-rf	0.41	0.05	−0.28	0.13	8.02
SMB	1.73	0.06	−0.23	0.15	29.55
HML	0.22	0.05	−0.13	0.14	4.77
CMA	0.00	0.03	−0.07	0.09	−0.12
RMW	0.44	0.03	−0.11	0.09	12.81
RD	2.10	0.20	−1.10	0.52	10.39

Source: Researchers’ computation

Table 5.

Correlation matrix

	Rm-rf	SMB	HML	RMW	CMA	RD	VIF
RM-RF	1						3.12
SMB	0.2423	1					2.3
HML	0.5589	0.2779	1				2.84
RMW	−0.4329	−0.3205	−0.2263	1			1.68
CMA	0.2723	0.25	0.3054	0.2743	1		1.55
RD	0.5147	0.4081	0.5675	−0.0469	0.1441	1	2.7

Source: Researchers’ computation

Table 6.

Factor spanning test

	RM	SMB	HML	CMA	RMW	RD	Intercept
RM		−0.15 (0.009)	−0.05 (0.48)	−0.15 (0.096)	−0.13 (0.15)	0.26 (0.00)	0.19** (0.04)
SMB	−0.39 (0.009)		0.39 (0.002)	−0.24 (0.009)	0.14 (0.31)	0.25 (0.00)	0.012* (0.001)
HML	−0.075 (0.48)	0.19 (0.002)		0.33 (0.001)	−0.23 (0.015)	0.098 (0.004)	0.019** (0.047)
CMA	−0.16 (0.096)	−0.104 (0.09)	0.29 (0.001)		−0.26 (0.003)	0.049 (0.12)	0.019 (0.76)
RMW	−0.15 (0.15)	0.066 (0.31)	−0.22 (0.015)	−0.29 (0.003)		−0.017 (0.62)	0.047 (0.075)
RD	0.41 (0.00)	0.22 (0.03)	0.72 (0.004)	0.09 (0.12)	−0.13 (0.62)		0.0134* (0.004)

Notes:

*,

**shows significance at the 1, 5 and 10%, respectively

Source: Researcher’s computation

Table 7.

GRS test result

	Mean alpha	GRS test	p-value	Mean SE	Mean abs a∼a	Mean adjusted R2
4 Distress sorted portfolio
MKT SMB HML	0.21	2.08	0.08	0.37	0.40	0.88
MKT SMB HML RD	0.04	1.96	0.11	0.31	0.44	0.91
MKT SMB HML CMA RMW	0.06	1.67	0.16	0.04	0.27	0.89
MKT SMB HML CMA RMW RD	0.02	1.59	0.18	0.03	0.32	0.92

Source: Researchers’ computation

Table 8.

Mean monthly percent excess returns for portfolios formed on a distress basis (October 2012–September 2022, 120 observations). Portfolios are rebalanced once a year. Using the Newey–West estimator, t-statistics are corrected for heteroscedasticity and autocorrelation up to four lags

Portfolios	P1	P2	P3	P4	P4 – P1
Mean	0.015**	0.021**	0.022*	0.037**	0.022**
t-stat	(1.96)	(2.26)	(3.88)	(2.46)	(2.50)

Note:

*,

**shows significance at the 1, and 5%, respectively

Source: Researchers’ computation

Table 9.

Mean monthly excess returns for portfolio formed on a distress basis (October 2012–September 2022, 120 observations). Portfolios are rebalanced once a year. Using the Newey–West estimator, t-statistics are corrected for heteroscedasticity and autocorrelation up to four lags

Asset pricing model	Test portfolio	Α	β	SMB	HML	CMA	RMW	RD
Fama–French three-factor model	P1	0.04** (2.43)	1.59* (22.65)	0.34* (3.67)	−0.53* (−4.65)
	P2	0.062** (2.11)	1.58* (18.12)	0.503* (5.37)	−0.11 (−1.14)
	P3	0.02 (0.52)	1.68* (21.84)	0.72* (6.50)	0.21 (1.77)
	P4	−0.038** (−1.20)	1.86* (16.56)	0.59* (5.67)	0.87* (6.43)
Augmented Fama–French three-factor model	P1	0.054** (2.21)	1.16* (10.13)	0.19 (1.75)	−0.7* (−6.33)			0.17 (1.57)
	P2	0.076* (2.72)	1.00* (8.99)	0.29* (3.15)	−0.34* (−3.45)			0.24* (5.41)
	P3	0.031 (0.91)	1.08* (7.58)	0.51* (4.39)	−0.16 (−0.15)			0.24* (5.48)
	P4	0.014 (0.49)	0.91* (6.23)	0.25* (3.97)	0.49* (3.99)			0.37* (9.06)
Fama–French five-factor model	P1	0.0017 (0.51)	1.69* (21.17)	0.29* (3.58)	−0.29** (−2.28)	−0.089 (−0.91)	0.57* (3.85)
	P2	0.044 (0.32)	1.65* (0.00)	0.47* (0.00)	0.07 (0.59)	−0.11 (0.32)	0.38** (3.86)
	P3	0.05 (0.12)	1.73* (20.27)	0.72* (6.54)	0.19 (1.14)	0.28** (2.20)	0.27 (1.58)
	P4	−0.041 (−1.12)	1.87* (12.74)	0.6* (4.87)	0.81* (4.09)	0.19 (1.69)	0.062 (0.21)
Augmented Fama–French five-factor model	P1	0.029** (2.38)	1.19* (11.22)	0.101 (0.19)	−0.44* (0.00)	−0.18 (0.09)	0.59* (0.00)	0.21 (0.23)
	P2	0.016** (2.44)	1.02* (11.78)	0.22* (3.78)	−0.12 (−1.14)	−0.22** (−2.21)	0.42* (3.92)	0.26* (9.28)
	P3	0.019 (0.51)	1.14* (7.82)	0.49* (4.29)	0.018 (0.16)	0.17 (1.66)	0.30** (2.46)	0.24* (5.35)
	P4	0.014 (1.57)	0.93* (5.78)	0.24* (3.64)	0.52* (3.52)	0.302 (0.27)	0.11 (0.73)	0.39* (8.96)

Note:

*,

**shows significance at the 1, and 5%, respectively

Source: Researchers’ computation

	Model	Regression
1	Fama–French five-factor model	(Ri-Rf) t = α + b1 (Rm-Rf) t + b2SMBt + b3HMLt + b4CMAt + b5RMWt + eit
2	Augmented Fama–French five-factor model	(Ri-Rf) t = α + b1 (Rm-Rf) t + b2SMBt + b3HMLt + b4CMAt + b5RMWt + b6RD + eit